This thesis concerns the development of computational methods for efficient flexible-aircraft flight dynamics analyses. An argument is made for a hierarchy of methods that provide predictive capability for loads and stability analyses, and the ability to create low-order dynamic models for control system synthesis. The proposed aeroelastic models are formulated using three-dimensional unsteady aerodynamics in the form of an unsteady vortex-lattice method developed to model the relatively complex kinematics inherent in flexible-aircraft dynamics, and in particular the unsteady induced drag. No assumptions are made relating to the kine- matics of the fluid-structure interface (inputs) and use of the three-dimensional Joukowski relation naturally resolves all components of the unsteady aerodynamic forcing (outputs). A consistent linearization of this method about an arbitrary reference state yields nondimen- sional (independent of free-stream dynamic pressure) discrete-time state-space models that resolve frequencies up to a spatio-temporal Nyquist limit defined by the wake discretization, and have a convenient form for coupling with structural dynamics models. Aircraft structural components are modelled using a geometrically-exact composite beam formulation, and, additionally, in the case of linear dynamics, a generic modal description. The latter allows the linear aerodynamics to be expressed in a reduced set of inputs and outputs, thus obtaining a time-domain alternative to the classical frequency-domain-based doublet-lattice method. The models modified for these modal degrees-of-freedom are shown to be amenable to balanced realization and truncation, and are verified in flutter analyses where only 10-100 balanced states are required (compared to 1000-10,000 physical states) for converged results. Finally, predictive controllers and linear-quadratic regulators are synthesized using reduced-order aeroelastic models, and are applied in nonlinear simulations for gust-load alleviation.